Indices, Logarithms and Surds
GCE Mathematics

(a) Solve for x in the equation: 3^(2x+1) - 26(3^x) - 9 = 0. [6 marks] (b) Given that log(base 2)(y + 3) + log(base 2)(y - 3) = log(base 2)(7y - 3), find the value of y. [5 marks] (c) Simplify: (sqrt(…

(a) Evaluate without using tables or calculator: log(base 10)(0.0625) + log(base 10)(160), giving your answer as a whole number. [4 marks] (b) (i) Show that (2^n * 9^(n+1)) / (6^(2n) * 3^(1-n)) simpli…

Simplify $\frac{\sqrt{3}}{\sqrt{3} - 1}$, rationalising the denominator.

Solve for $x$: $4^x = 8^{x-1}$

Evaluate $3^{-2} \times 27^{\frac{2}{3}}$

Simplify $\frac{5\sqrt{2} + \sqrt{50}}{\sqrt{8}}$.

Given that $\log_3(x^2 - 2x) = 1$, find the possible values of $x$.

If $\log_x 64 = 3$, find the value of $x$.

If $\log_{10} 2 = 0.3010$ and $\log_{10} 3 = 0.4771$, find $\log_{10} 72$.